1. Field of the Invention
This invention relates generally to a method and apparatus for detecting and identifying excessively vibrating blades in a turbomachine and, more particularly, to such a method and apparatus which is employed while the turbomachine is operating.
2. Description of the Prior Art
It is generally known that turbomachinery blade failures are a major problem and, particularly in the steam turbine generator area, are the cause of many forced outages for U.S. electrical generating utilities. In the early stages of most blade failures, the blade will experience cracks, which may be the result of high cycle fatigue or stress corrosion combined with fatigue. In either event, it is undesirable and excessive blade vibration that leads to the formation of a fatigue crack and to eventual blade failure.
High amplitude, resonant, order related blade vibration results when one of the forcing frequencies that act on a rotating turbomachinery blade coincides with one of the blade's many natural frequencies. In a turbine, the forcing frequencies which may cause such excessive blade vibration comprise all of the multiples of nozzle passing frequency, and all of the multiples of running speed. The former arise from the series of kicks that each blade receives in passing the nozzle wakes, while the latter are due to flow non-uniformities arising from the horizontal split of the nozzle diaphragms and casing, internal struts, inlet or exhaust openings, nozzle plates, or the like. In each case, the multiples, or harmonics of the fundamental forcing frequency are caused by the non-sinusoidal nature of the forcing waveform. Obviously, for a constant speed turbine, the values of all these forcing frequencies are precisely known for each blade stage.
This is not the case, however, for the natural frequencies of the various blades. Here, uncertainties in the degree of fixity between fastener and wheel or tenon and shroud, and the necessity for empirical estimations as to the effects of centrifugal loading, all lead to uncertainties in the predicted values of the natural frequencies of the blades. in addition, normal manufacturing and assembly tolerances lead to variations from one blade to the next. Since the most predictable modes are the lower frequency modes, and since they are also the modes most likely to be subjected to high amplitude excitation, they are the ones that manufacturers concentrate on in attempting to avoid such resonant matches.
Actual vibration amplitudes in a resonant match of one of the forcing frequencies with one of the natural frequencies of the blade depend on the level of the input at the forcing frequency, on the mode shape and amplification factor of the affected mode, and on the degree of match between the natural frequency and the forcing frequency. When the two frequencies differ, the vibration occurs at the forcing frequency, not the natural frequency. For example, in some steam turbine blade modes, amplification factors as high as 400 are not uncommon. In addition to indicating the level of increase in amplitude for an exact resonant match, the amplification factor indicates how the vibration amplitude varies with the degree of match. For example, for just a 1% difference between the forcing frequency and the natural frequency, the vibration amplitude drops 25% of its full resonant value for an amplification factor of 200, and to 12% of its full resonant value for an amplification factor of 400. Thus, although the high amplification factor modes are potentially more damaging, they require a more perfect frequency match to excite them at their most damaging levels. Therefore, it is apparent that due to the previously mentioned variation in the natural frequencies blade to blade, only a few of the blades or blade groups in a given blade row of the rotating portion of a turbo machine might undergo excessive, high amplitude vibration at a given time.
The extreme sensitivity to the degree of match between the forcing and natural frequencies for high amplification factor modes has still another potential benefit. If a resonantly vibrating blade develops a fatigue crack, it is likely that the affected natural frequency will be shifted by 1% or more. As indicated above, the accompanying reduction in amplitude should be significant and can be used as one indicator of the initiation of a crack. Thus, a monitoring system that can measure individual resonant blade vibrations, is also able to indicate crack inception and growth. However, the primary purpose of such a system is to detect and identify excessively vibrating blades so that such blade may be replaced before actual fatigue cracking occurs. In this manner, the turbomachine may be operated in a safer, more efficient manner while avoiding the inconvenient and expensive outages which may result from unanticipated turbine blade failures.